Degeneracy study of the forward kinematics of planar 3-RPR parallel manipulators

Philippe Wenger (1) , Damien Chablat (1) , Mazen Zein (1)

1 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes

This paper investigates two situations in which the forward kinematics of planar 3-RPR parallel manipulators degenerates. These situations have not been addressed before. The first degeneracy arises when the three input joint variables r1, r2 and r3 satisfy a certain relationship. This degeneracy yields a double root of the characteristic polynomial in t, which could be erroneously interpreted as two coalesce assembly modes. But, unlike what arises in non-degenerate cases, this double root yields two sets of solutions for the position coordinates (x, y) of the platform. In the second situation, we show that the forward kinematics degenerates over the whole joint space if the base and platform triangles are congruent and the platform triangle is rotated by 180 deg about one of its sides. For these "degenerate" manipulators, which are defined here for the first time, the forward kinematics is reduced to the solution of a 3rd-degree polynomial and a quadratics in sequence. Such manipulators constitute, in turn, a new family of analytic planar manipulators that would be more suitable for industrial applications.

Mots clés: 3RPR parallel mechanism; direct kinematics; forward kinematics; analytic manipulators

Domaines: Robotique [cs.RO]

Philippe Wenger, Damien Chablat, Mazen Zein. Degeneracy study of the forward kinematics of planar 3-RPR parallel manipulators. Journal of Mechanical Design, 2007, 129 (12), pp.1-6. ⟨hal-00162649⟩